9 problems

Let $A$ be a finite-dimensional algebra over a field $K$, and let $\operatorname{\mathsf{mod}} A$ denote its category of finitely generated modules. A torsion class…

Let $\Lambda$ be a finite-dimensional algebra. The group $\operatorname{\mathrm{int}\text{-}\mathrm{heart}}(\operatorname{tors}\Lambda)$ has heart-controlled generators, meaning th…

Non-increasing cover conjecture. If

Jordan--Hölder criterion. The maximal green sequences … have the same set of bricks if and only if they are equivalent.

Wall-dimension conjecture. For each $\theta\in K_0(\operatorname{\mathsf{proj}} A)$, we have

TF-class canonical decomposition conjecture. For each $\theta\in K_0(\operatorname{\mathsf{proj}} A)$, we have

Let $(A,\mathcal{C})$ be an almost-directed $d$-homological pair, meaning that $A$ is an algebra equipped with the subcategory $\mathcal{C}$, and suppose that … A $d$-strong torsio…

Let $\Lambda$ be an associative algebra, and suppose that its functorially finite torsion classes form a lattice under inclusion. Congruence-uniformity conjecture. That lattice is…

Let $Q$ be a quiver with compatible ordering of its vertices, let $c=s_1s_2\cdots s_n$ be the corresponding Coxeter element, and let $W$ be its Weyl group. For $w\in W$, let $I_w$…